A swimming coach wants to know whether swimmers showed improvement in 100 meters freestyle event ...

A swimming coach wants to know whether swimmers showed improvement in 100 meters freestyle event after attending a central training camp. As such, 12 swimmers were selected at random and their times were recorded twice: best time before attending the training camp and best time after attending the training camp. The objective of the study is to see whether the times recorded are faster (lower) after attending the training camp as compared to before attending. The times recorded (in seconds) are shown in Table 1.

Table 1

Swimmer

Before

After

1

81.32

76.48

2

69.35

66.18

3

70.65

65.15

4

77.53

74.82

5

86.68

77.69

6

75.37

69.42

7

68.43

67.34

8

64.10

55.17

9

83.28

87.40

10

88.85

84.73

11

61.47

59.34

12

99.96

82.04
  1. Calculate the mean time difference after and before attending the training camp.
  2. Calculate the standard deviation time difference after and before attending the training camp.
  3. What assumptions should be made to conduct the hypothesis test?
  4. At a = 0.05, can you support the claim that the mean time after attending the training camp is lower as compared to before attending the training camp? Assume the population variances are equal.

Solved
SCIENCE/MATH 1 Answer Leah Jane Aying

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